Skip to main content

Full text of "Mathematical And Physical Papers - Iii"

See other formats


ON THE MOTION OF PENDULUMS.
103
resistance than if it had started from the same position with the fluid at rest. In fact, it appears from the expression for G in Art. 8, that the moment of the resistance vanishes, in passing from negative to positive, not when the disk has reached the end of its excursion in the positive direction, but the eighth part of a period earlier. Hence, had the observation commenced during a series of oscillations, a larger initial arc would have been necessary, to overcome the greater resistance, in order to produce, after a given number of oscillations, the same final arc as that actually observed. I have investigated the correction to be applied on account of this cause, and find it to be about + 0*009, but I must refer to a note for the demonstration, in order not to interrupt the present discussion*. I shall assume then, in the following comparisons, that for water
V//= 0-0564,
the units being the sam^e as before, namely, an English inch and a second. That p! is independent of the pressure of the fluid, or at least very nearly so, appears from an experiment of Coulomb's, in which it was found that the decrement of the arc of oscillation of a disk oscillating in water was the same in an exhausted receiver as under the full atmospheric pressure.
I will here mention another experiment of Coulomb's which bears directly on one part of the theory. On covering the disk with a thin coating of tallow, the resistance was found to be the same as before; and even when the tallow was sprinkled with powdered sandstone, by means of a sieve, the increase of resistance was barely sensible. This strikingly confirms the correctness of the equations of condition assumed to hold good at the surface of a solid.
66. I will now compare the formula (148) with the results obtained by Bessel for the oscillations of the brass sphere in water, which will be found at page 65 of his memoir. This sphere was suspended so as to be immersed in the water contained in a lar^e vessel, and was swung with two different lengths of wire, the same as those employed for the experiments in air. The times of oscillation were T90S5 second for the long pendulum, and T1078 for the short. The results are
I
;
See note B. at the end.